Anomalous dimension: quantum loop corrections cause fields to scale differently from their classical (canonical) dimension.
Scalar field φ classically scales as [φ] = (d−2)/2. With interactions, the propagator acquires anomalous dimension η: G(k) ~ k−2+η.
This shifts critical exponents away from mean-field values: ν = 1/(2−η) changes to the non-trivial value. For the 3D Ising model, η ≈ 0.0363 (known to 5 decimal places from conformal bootstrap).
The β-function governs how the coupling runs: β(g) = μ dg/dμ. Fixed points (β=0) are where scale invariance holds — these give conformal field theories.